Question: The sum of two numbers is $123$, and their difference is $53$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 123}$ ${x-y = 53}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 176 $ $ x = \dfrac{176}{2} $ ${x = 88}$ Now that you know ${x = 88}$ , plug it back into $ {x+y = 123}$ to find $y$ ${(88)}{ + y = 123}$ ${y = 35}$ You can also plug ${x = 88}$ into $ {x-y = 53}$ and get the same answer for $y$ ${(88)}{ - y = 53}$ ${y = 35}$ Therefore, the larger number is $88$, and the smaller number is $35$.